Column
Left Right
Up -1,-1 -10,0
ROW
Down 0, -10 -8, -8
1.4 Do you recognize this game from your reading or the lecture?
You can do a linear transformation on the
payoffs of a game without changing its essential structure. In
fact, you can even do more general monotonic
transformations, though that will affect the probabilities in a
mixed strategy equilibrium. Which game is disguised under the
action names of Game 1? For the answer, click here
A linear transformation take each payoff combination X, Y and transforms it to a+bX, a+bY. Here, let us insist that b be positive, tho a could be negative. Thus, with a=100 and b=2, the game above becomes GAME 1a
Column
Left Right
Up 98,98 80,100
ROW
Down 100, 80 84,84
Game 1a and Game 1 are essentially the same.
Return to Self Test 1.